Station 1 - MS. STRAWSKA'S WEBSITE - Home



Station 1

[pic]

Graph the Following Inequalities:

1. 7 < f

2. [pic]

3. [pic]

4. x > -3

Word Problem:

Twelve prizes were raffled off by the band to raise money for new uniforms. All of the prizes were valued at $25 or more.

Write and graph and inequality for the situation above.

Station 2

[pic]

Match Each of the Following Inequalities with its Graph:

1. x < 2 2. 1 < x 3. [pic]

4. [pic] 5. [pic]

A.

[pic]

B.

B.

[pic][pic]

C.

[pic]

D.

[pic]

[pic]

E.

[pic]

Word Problem:

Jared spent at least $135 on tickets to the Red Sox game.

Write and graph an inequality for the situation above.

Station 3

[pic]

Write an Inequality for Each of the Following Graphs:

1. [pic]

2. [pic]

3. [pic]

4. [pic]

Word Problem:

When the quarter back was sacked during last night’s game, there was a loss of more than 6 yards on the play.

Write and graph an inequality for the situation above.

Station 4

[pic]

Solve and Graph the Following Inequalities:

1. 9 < x + 5

2. c + 12 > 7

3. [pic]

4. [pic]

Word Problem:

Less than 39 of the orange trees were lost during the frost last month.

Write and graph an inequality for the situation above.

Station 5

[pic]

Solve and Graph the Following Inequalities:

1. -3 < x - 15

2. n - 8 > -2

3. [pic]

4. [pic]

Word Problem:

Fewer than 63 of the students surveyed said that they read for 30 minutes or more per night.

Write and graph an inequality for the situation above.

Station 6

[pic]

Find the Error(s) Made When Solving and Graphing Each of the Following Inequalities:

x – 5 > 12

– 5 – 5

x > 7

[pic]

1. 3 < x + 2

– 3 – 3

– 1 < x or x > – 1

[pic]

Word Problem:

Sarah bought at least 15 cases of soda to sell during the dance.

Write and graph an inequality for the situation above.

Station 7

[pic]

Solve Each of the Following Inequalities:

1. 5x < 105

2. [pic]

3. [pic]

4. – 9x < 108

5. 12x > – 48

Word Problem:

Compare and contrast solving a one-step equation and a one-step inequality.

Station 8

[pic]

Find the Error Made When Solving and Graphing Each of the Following Inequalities:

4x > -8

4 4

x < -2

[pic]

1. [pic]

× -3 × -3

[pic]

[pic]

Word Problem:

What does a closed dot above a number mean?

What does an open dot above a number mean?

Station 9

[pic]

Solve and Graph the Following Inequalities:

1. 2x + 3 > 25

2. [pic]

3. [pic]

4. 4(x + 2) – 7 > 65

5. [pic]

Word Problem:

Ralph has a total of $23. He needs to buy a bag of food for his dog which costs $13.69. He also wants to buy some grapes that cost $1.89 per pound. Write and solve an inequality for the number of pounds of grapes Ralph can buy.

Station 10

[pic]

Solve and Graph the Following Inequalities:

1. [pic]

2. 5x – 14 > 8x + 4

3. [pic]

4. [pic]

5. 3(1 – 3x) < 2(7 – 4x)

Word Problem:

Wendy charges $7 per hour for babysitting plus $5 for snacks and drinks. Patti charges $5 per hour plus $8 for snacks and drinks. Write and solve and inequality to find how many hours Wendy charges less than Patti?

Station 11

[pic]

Find the error(s) made when solving and graphing each inequality:

1. 2x – 5 > 12

÷2 ÷2

x – 5 > 6

+5 +5

x > 11

Word Problem:

Explain to a friend who is struggling how to solve and graph 3x + 2 < 5x – 6

Station 12

[pic]

Find the error(s) made when solving and graphing the following inequalities:

1. 5x + 6 < 3x + 2

- 2 - 2

5x + 4 < 3x

+ 5x + 5x

4 < 8x

÷ 8 ÷ 8

½ < x

Word Problem:

Mattie owns a catering company. She charges a fee of $500 plus $10 per plate for weddings. Her rival company charges a fee of $450 plus $15 per plate. Write and solve an inequality for when Mattie will charge less than her competitor.

Station 1:

1. 2. 3.

4. Word Problem:

Station 2:

1. 2. 3.

4. 5. Word Problem:

Station 3:

1. 2. 3.

4. Word Problem:

Station 4:

1. 2. 3.

4. Word Problem:

Station 5:

1. 2. 3.

4. Word Problem:

Station 6:

1. 2.

Word Problem:

Station 7:

1. 2. 3.

4. 5. Word Problem:

Station 8:

1. 2.

Word Problem:

Station 9:

1. 2. 3.

4. 5. Word Problem:

Station 10:

1. 2. 3.

4. 5. Word Problem:

Station 11:

1. 2.

Word Problem:

Station 12:

1. 2.

Word Problem:

Station 1 Key:

1. 2. 3.

4. Word Problem: p ≥ 25

Station 2 Key:

1. C 2. D 3. A

4. E 5. B Word Problem: t ≥ 135

Station 3 Key:

1. x > 2 2. x ≥ - 4 3. x < 5

4. x ≥ - 1 Word Problem: L > 6

Station 4 Key:

1. x > 4 2. c > - 5 3. g ≥ 103

4. p ≥ -22 Word Problem: t < 39

Station 5 Key:

1. x > 12 2. n > 6 3. k ≥ 45

4. p ≥ 156 Word Problem: s < 63

Station 6 Key:

1. 5 should be added not subtracted, the dot should be open

2. should subtract 2 not 3, dot should be above 1 not – 1

Word Problem: s ≥ 15

Station 7 Key:

1. x < 21 2. h ≥ - 18 3. k ≤ 12

4. x > - 12 5. x > - 4

Word Problem: The steps are the same for solving an equation and inequality. The difference among them is that you need to remember to change the sign when you multiply or divide by a negative number.

Station 8 Key:

1. The sign should not have been changed because you divide by a positive.

2. The sign should be changed because you multiply by a negative.

Word Problem:

Closed dot: the number is part of the solution set

Open dot: the number is not part of the solution set

Station 9:

1. x > 11

2. x ≥ - 7

3. x < -10/3

4. x > 16

5. x ≤ 31

Word Problem: 1.89g + 13.69 ≤ 23, g ≤ 4.925

Station 10:

1. x ≤ 0

2. x < - 6

3. x < -1

4. x ≥ 4

5. x > - 11

Word Problem: 7x + 5 < 5x + 8, x < 1.5

Station 11:

1. 5 should be added first, then divide by 2. The dot should be on 17/2 or 8.5

2. 2 should be subtracted first, then multiply by 3. The dot should be open and on 9. The arrow should point to the right.

Word Problem: (Sample Answer) Since the variable appears on both sides of the inequality you need to move one of them to the other side. I would move the 3x to the right by subtracting it on both sides of the inequality. You could also move 5x by subtracting it, but then you would be working with a negative variable which is a little bit more difficult. After subtracting 3x from both sides, the equivalent inequality would be 2 < 2x – 6. Now that the variable is on only one side of the inequality, the next step is to undo addition or subtraction. Since 6 is being subtracted, it is undone by using the inverse operation, addition. After adding 6 to both sides of the inequality, the equivalent inequality is 8 < 2x. The final step to solve this inequality is to undo the multiplication by dividing both sides of the inequality by 2. The solved inequality is 4 < x. To graph the inequality, put an open dot on 4 on the number line. The dot is open to show that 4 is not included in the solution set. Since x is more than 4, draw an arrow pointing to the right to show that values above 4 are the solutions to the inequality.

Station 12:

1. 5x should be subtracted not added. The dot should be on – 2. The arrow should point to the left.

2. 3 should have also been distributed to the 2. The dot should be on – 6.

Word Problem: 10x + 500 < 15x + 450, x > 10

-----------------------

–25

–20

–15

–10

–5

25

20

15

10

5

0

0

–1

–2

–3

–4

–5

5

4

3

2

1

0

-5 -4 -3 -2 -1 0 1 2 3 4 5

0

0

0

0

0

7

– 1

0

0

– 15

0

2. [pic] + 2 > 5

×3 ×3

x + 2 > 10

- 2 - 2

x > 8

0 8

0 11

2. 3(x

+ 2) ≤ 2x

3x + 2 ≤ 2x

- 2x - 2x

x + 2 ≤ 0

-2 -2

x ≤ -2

0 1/2

-2 0

- 4 0

0 12

7

0

- 3 4

0 25

0 135

0 6

0 4 - 5 0 0 103

- 22 0 0 39

0 12 0 6 0 45

0 156 0 63

0 15

0. 11

- 7 0

-10/3 0

0. 16

0 31

0. 1

-6 0

-1 0

0. 4

-11 0

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